Question

the figures shown are similar. find the lengths of x, y, and z.
the length of side x is \square.
(type an integer or a decimal.)

Explanation:

Step1: Determine the scale factor

The corresponding sides of similar figures are proportional. The side of length 4 in the larger figure corresponds to the side of length 3 in the smaller figure? Wait, no, wait. Wait, the larger figure has a side of 4? Wait, no, looking at the figures: the smaller figure has a side of 3, and the larger figure has a side of 4? Wait, no, the larger figure has a side of 4, and the smaller has 3? Wait, no, the larger figure has a side of 7, and the smaller has x? Wait, no, let's check the sides. The larger figure: vertical side 7, bottom side 7, slant side 8, and the other side 4. The smaller figure: vertical side x, bottom side z, slant side y, and the other side 3. So the side of length 4 in the larger corresponds to 3 in the smaller? Wait, no, 4 and 3? Wait, no, maybe the side of length 4 in the larger is corresponding to 3 in the smaller. So the scale factor from larger to smaller is 3/4? Wait, no, similar figures: the ratio of corresponding sides is equal. So let's find the corresponding sides. Let's see, the larger figure has a side of 4, and the smaller has 3. So 4 corresponds to 3? Wait, no, maybe the larger figure's side of 4 corresponds to the smaller's 3. Then the scale factor is 3/4. Then the vertical side of the larger is 7, so the vertical side of the smaller (x) would be 7(3/4)? Wait, no, that doesn't make sense. Wait, maybe the larger figure's side of 7 corresponds to the smaller's x? Wait, no, let's check again. Wait, the larger figure: sides 7 (left), 7 (bottom), 8 (slant), 4 (right). The smaller figure: sides x (left), z (bottom), y (slant), 3 (right). So the right side of the larger is 4, right side of smaller is 3. So the ratio of smaller to larger is 3/4. So all sides of the smaller are 3/4 of the larger. So the left side of the larger is 7, so the left side of the smaller (x) is 7(3/4)? Wait, no, 7(3/4) is 5.25? Wait, but let's check: 4(3/4)=3, which matches the smaller's right side. Yes! So the right side of larger is 4, smaller is 3: 4(3/4)=3. So the scale factor from larger to smaller is 3/4. Therefore, the left side of larger is 7, so left side of smaller (x) is 7(3/4) = 5.25? Wait, but 7(3/4) is 5.25. Wait, but let's confirm. So 4 (larger right) (3/4) = 3 (smaller right). Correct. Then 7 (larger left) (3/4) = x. So 7(3/4) = 5.25. So x = 5.25.

Step2: Calculate x

x = 7 * (3/4) = 5.25

Answer:

5.25